Diameter of Polyhedra: Limits of Abstraction

• Published in: Mathematics of Operations Research (ISSN: 1526-5471), vol. 35, num. 4, p. 786-794
• Publication date: 2010

We investigate the diameter of a natural abstraction of the 1-skeleton of polyhedra. Even if this abstraction is more general than other abstractions previously studied in the literature, known upper bounds on the diameter of polyhedra continue to hold here. On the other hand, we show that this abstraction has its limits by providing an almost quadratic lower bound.

Keywords: convex geometry ; disjoint coverings ; Hirsch conjecture ; polyhedra ; D-Step Conjecture ; Simplex Algorithm ; Polytopes ; Graphs ; Cubes

Reference

• EPFL-ARTICLE-164208
• doi:10.1287/moor.1100.0470
• View record in Web of Science

Record created on 2011-03-10, modified on 2012-03-21